ALGEBRA II SEMESTER EXAM REVIEW

Domain and Range

The set of all possible input values (x) and the corresponding output values (y) of a function.

End Behavior

Describes what happens to y-values as x approaches positive or negative infinity.

Vertex Form of a Quadratic Function

y = a(x - h)² + k, where (h, k) is the vertex of the parabola.

Discriminant Formula

D = b² - 4ac, used to determine the nature of the roots of a quadratic equation.

Complex Numbers

Numbers that have a real part and an imaginary part, expressed as a + bi.

Quadratic Formula

x = (-b ± √(b² - 4ac)) / (2a), used to find the roots of a quadratic equation.

Transformations of Functions

Changes to the graph of a function, including shifts, stretches, and reflections.

Inequality Notation

A way to describe the set of solutions that satisfy an inequality using symbols like ≤ or ≥.

Factoring Polynomials

The process of breaking down a polynomial into simpler components that, when multiplied together, give the original polynomial.

Systems of Equations

A set of equations with the same variables that are solved together.

Conic Sections

The curves obtained by intersecting a plane with a double-napped cone, including parabolas, circles, ellipses, and hyperbolas.

Quadratic Inequalities

Inequalities that involve quadratic expressions, often solved by finding intervals on a number line.

Absolute Value Function

A function that describes the distance of a number from zero, expressed as f(x) = |x|.

Polynomial Division

The process of dividing one polynomial by another, which can be done using long division or synthetic division.

Factoring by Grouping

A method of factoring polynomials with four terms by grouping pairs of terms together.

Asymptotes

Lines that a graph approaches but never touches, indicating behavior as it tends toward infinity.

Roots of a Quadratic Function

The values of x for which the quadratic function equals zero, found using the quadratic formula or factoring.

Vertex of a Parabola

The highest or lowest point on the graph of a quadratic function, represented by the coordinates (h, k).

Standard Form of a Quadratic Function

The form of a quadratic function written as y = ax² + bx + c.

Vertical Stretch and Compression

Changes in the steepness of the graph of a function, caused by multiplying the output of the function by a factor.

Horizontal Stretch and Compression

Changes in the width of the graph of a function, caused by multiplying the input of the function by a factor.

Zeroes of a Function

The x-values where the function's output is zero, also known as the x-intercepts.

Intercepts

Points where a graph crosses the x-axis (x-intercepts) or y-axis (y-intercept).

Quadratic Regression

A statistical method used to fit a quadratic equation to a set of data points.

Polynomial Functions

Functions that are represented by a polynomial equation, which can have one or more terms.